Question

Comparing Gas Mileages. An experiment is to be conducted to compare four different brands of gasoline for gas mileage.

(a) Suppose that you randomly divide 24 cars into four groups of 6 cars each and then randomly assign the four groups to the four brands of gasoline, one group per brand. Is this experimental design a completely randomized design or a randomized block design? If it is the latter, what are the blocks?

(b) Suppose, instead, that you use six different models of cars whose varying characteristics (e.g., weight and horsepower) affect gas mileage. Four cars of each model are randomly assigned to the four different brands of gasoline. Is this experimental design a completely randomized design or a randomized block design? If it is the latter, what are the blocks?

(c) Which design is better, the one in part (a) or the one in part (b)? Explain your answer.

Short answer

Part (a) Completely randomized design

Part (b) Randomized block design

Part (c) Randomized block design is better.

Step-by-step solution

Part (a) Step 1. Given information.

In the question, it is given that an experiment is to be conducted to compare four different brands of gasoline for gas mileage.

Part (a) Step 2. Identify if the experimental design is a completely randomized design or a randomized block design.

As we can observe from the given experimental design that 24 cars were divided into four groups of 6 cars each and then randomly assign the four groups to the four brands of gasoline in a way that it will result in one group per brand.

Therefore, this statement makes the experimental design a completely randomized design because the experimental units are assigned randomly among all of the treatments in this study.

Part (b) Step 1. Identify if the experimental design is a completely randomized design or a randomized block design.

As we can observe from the given experimental design we are using here six different models of cars whose varying characteristics affect gas mileage.

Here the four cars of each model are randomly assigned to the four different brands of gasoline.

Therefore, this statement makes the experimental design a randomized block design because the experimental units are randomly assigned among all the treatments separately within each block.

Part (c) Step 1. Decide which design is better.

Part (b) of the randomized block design is superior because the experimental units (cars) that are comparable in some aspects (weight, horsepower, etc.) and are expected to affect the response variable (gas mileage) are grouped together in blocks.